10
LTC4400-1/LTC4400-2
sn4400 4400fas
Determining External Loop Gain and Bandwidth
The external loop voltage gain contributed by the RF chan-
nel and RF feedback coupling network should be mea-
sured in a closed-loop configuration. A voltage step is
applied to PCTL and the change in V
PCA/B
is measured. The
detected voltage is K • PCTL, where K is the internal gain
between PCTL and the RF pin, and the external voltage gain
contributed by the RF power amplifier and RF feedback
coupling network is K • ∆V
PCTL
/∆V
VPC
. Measuring voltage
gain in the closed-loop configuration accounts for the
nonlinear detector gain that is dependent on RF input
voltage and frequency.
The LTC4400-X unity gain bandwidth specified in the data
sheet assumes that the net voltage gain contributed by the
RF power amplifier and RF feedback coupler is unity. The
bandwidth is calculated by measuring the rise time be-
tween 10% and 90% of the voltage change at V
PCA/B
for a
small step in voltage applied to PCTL.
BW1 = 0.35/rise time
The LTC4400-X control amplifier unity gain bandwidth
(BW1) is typically 450kHz below a PCTL voltage of 80mV.
For PCTL voltages <80mV, the RF detected voltage is
0.6PCTL. For PCTL voltages >160mV, RF detected voltage
is 1.22PCTL – 0.1. This change in gain is due to an internal
compression circuit designed to extend the detector range.
For example, to determine the external RF channel loop
voltage gain with the loop closed, apply a 100mV step to
PCTL from 300mV to 400mV. V
PCA/B
will increase to
APPLICATIO S I FOR ATIO
WUUU
supply enough feedback voltage to the RF pin to cancel
this 100mV step which would be the required detected
voltage step of 122mV. V
PCA/B
changed from 1.5V to
1.561V to create the RF output power change required.
The net external voltage gain contributed by the RF power
amplifier and RF feedback coupling network can be calcu-
lated by dividing the 122mV change at the RF pin by the
61mV change at the V
PCA/B
pin. The net external voltage
gain would then be approximately 2. The loop bandwidth
extends to 2 • BW1. If BW1 is 230kHz, the loop bandwidth
increases to approximately 460kHz. The phase margin can
be determined from Figures 2 and 3. Repeat the above
voltage gain measurement over the full power and fre-
quency range.
External pole frequencies within the loop will further
reduce phase margin. The phase margin degradation, due
to external and internal pole combinations, is difficult to
determine since complex poles are present. Gain peaking
may occur, resulting in higher bandwidth and lower phase
margin than predicted from the open-loop Bode plot. A
low frequency AC SPICE model of the LTC4400-X power
controller is included to better determine pole and zero
interactions. The user can apply external gains and poles
to determine bandwidth and phase margin. DC, transient
and RF information cannot be extracted from the present
model. The model is suitable for external gain evaluations
up to 6×. The 270kHz PCTL input filter limits the band-
width, therefore, use the RF input as demonstrated in the
model. Gain compression is not modeled.
Figure 2. Measured Open-Loop Gain and Phase, PCTL < 80mV Figure 3. Measured Open-Loop Gain and Phase, PCTL > 160mV
FREQUENCY (Hz)
100
–20
VOLTAGE GAIN (dB)
PHASE (DEG)
–10
0
20
10
40
30
1k 10k 100k 1M 10M
4400 F02
–30
–40
–50
–60
60
50
80
70
–20
0
20
60
40
100
80
–40
–60
–80
–100
–120
140
120
160
PHASE
GAIN
R
LOAD
= 2k
C
LOAD
= 33pF
FREQUENCY (Hz)
100
–20
VOLTAGE GAIN (dB)
PHASE (DEG)
–10
0
20
10
40
30
1k 10k 100k 1M 10M
4400 F03
–30
–40
–50
–60
60
50
80
70
–20
0
20
60
40
100
80
–40
–60
–80
–100
140
120
180
160
PHASE
R
LOAD
= 2k
C
LOAD
= 33pF
GAIN
